Comprehensive analysis of queue times in microelectronic manufacturing

ABSTRACT

A system for determining a group of semiconductor manufacturing process steps with a similar influence on individual semiconductor products. The system generates a first table including time stamps for the individual semiconductor products. The system creates a second table including Q-times based on the first table. The Q-times refers to time differences between every pair of the time stamps. The system forms a dependency table by grouping the Q-times with similar dependencies together. The system identifies groups of the similar dependencies. The system extracts semiconductor process steps belonging to the groups.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.12/778,457, filed May 12, 2010, the entire content and disclosure ofwhich is incorporated herein by reference.

BACKGROUND

The present application generally relates to manufacturing semiconductorproducts. More particularly, the present application relates todetermining a group of semiconductor manufacturing process steps with asimilar influence on individual semiconductor products.

A semiconductor product includes, but is not limited to a semiconductorchip, a semiconductor wafer, and a semiconductor wafer lot. A similarinfluence of queue time (“Q-time”) on individual semiconductor productsincludes, but is not limited to increasing or decreasing leakagecurrent, increasing or decreasing threshold voltage, increasing ordecreasing areas of the semiconductor products, increasing or decreasingoperational frequencies of the semiconductor products, etc. Q-timerefers to the time spent for a semiconductor product to wait betweenindividual semiconductor manufacturing processes. Maintaining highmanufacturing yields and precise product quality control are of utmostimportance in a commercial manufacture (e.g., IBM®, etc.) ofsemiconductor products. Unfortunately, an extraordinary sophisticationof individual fabrication processes and an extreme complexity of anoverall integrated fabrication process present myriad mechanisms fordefects to be introduced which may degrade semiconductor productperformance or render a semiconductor product non-functional. Thus,manufacturing yields are frequently lower than desired and productperformance distributions are wider than desired.

A vast scale and scope of defect generating mechanisms also lead toextreme difficulties in diagnosing a source of defects, and many defectsin semiconductor product manufacturing processes go undiagnosed. Forexample, a traditional diagnostic procedure may attempt a fullevaluation of entire parameters (e.g., leakage current, capacitance,frequency, area, etc.) in an entire semiconductor manufacturing process.However, any such attempt may involve an impossible amount of data andcombinatorially growing dependence structures (e.g., data dependency).Thus, to reduce the amount of computation, typical diagnostic ormonitoring methods focus on specific subsets of production data such asproduction logistics and/or process trace data. An example of productionlogistics data is that a semiconductor wafer “X” in a semiconductor lot“Y” at time “T1” entered a chamber “C” in a semiconductor manufacturingtool “A” where a semiconductor manufacturing process “P” following arecipe “R” was performed as a semiconductor manufacturing step “S” untiltime “T2”. Examples of the trace data include, but are not limited tochamber pressure, chamber temperature, and chamber atmospherecomposition.

Q-time can vary widely in a semiconductor manufacturing environment,reflecting different line loading and tool availabilities. Significantproduct defects can be associated with the queue times betweenparticular process steps in the semiconductor manufacturing process. Forexample, epitaxial thin film growth can be influenced by a pre-clean todeposition queue time, as a result of an uncontrolled growth of nativeoxides, especially on sidewalls. Back end metallization can sufferserious corrosion if a post-polish queue time is not maintained below acritical threshold. Migration of RIE (Reactive Ion Etching) inducedcontamination from photoresist is observed if an etch to strip queuetime is not controlled.

Traditionally, the discovery of these effects (i.e., Q-time effects onsemiconductor manufacturing process) has been a result of a painstakingad-hoc investigation of otherwise unexplainable aberrant manufacturingresults. Typically, it is difficult to anticipate an impact of queuetimes on some semiconductor manufacturing processes now in development.Traditionally, when discovered and adequately explored the Q-timeeffects, manufacturing line controls are introduced to assuresemiconductor manufacturing processes take place within acceptable queuetime windows.

Typical semiconductor manufacturing lines may include several thousandsof steps, representing as many as 1,000,000 queue times. While the queuetimes between some particular steps are known to be critical, ingeneral, product quality is not expected to be a sensitive function ofqueue time. These two factors (i.e., queue times and the productquality) contribute to a status quo in semiconductor productmanufacturing. By analyzing or monitoring the semiconductormanufacturing process, the impact of queue time on product qualityand/or manufacturing yields can be obtained, e.g., identifying pairs orgroups of semiconductor manufacturing process steps with dependent(i.e., correlated) Q-times, and hence pointing to a group of steps witha possible influence on the product quality.

SUMMARY OF THE INVENTION

The present disclosure describes a system and computer program productfor determining a group of semiconductor manufacturing process stepswith a similar influence on individual semiconductor products.

In one embodiment, there is provided a system for determining a group ofsemiconductor manufacturing process steps with a similar influence onindividual semiconductor products. The system comprises a memory deviceand a processor being connected to the memory device. The processorobtains a first table including time stamps of the manufacturing processsteps for the individual semiconductor products. The processor creates asecond table including Q-times based on the first table. The Q-timesrefers to time differences between every pair of the time stamps. Theprocessor forms a dependency table by grouping the Q-times with similardependencies together. The processor identifies groups of the similardependencies. The processor extracts semiconductor process stepsbelonging to the groups.

In a further embodiment, the dependency table includes a multi-modalcharacter. The multi-modal character refers to a graph or histogram of adistribution of a correlation having at least two distinct maxima.

In a further embodiment, the processor clusters the Q-times into thegroups of similar dependency measures.

In a further embodiment, the similar dependency measure includes similarcorrelation coefficients.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings are included to provide a furtherunderstanding of the present invention, and are incorporated in andconstitute a part of this specification.

FIG. 1 illustrates a flow chart illustrating method steps fordetermining a group of semiconductor manufacturing process steps with asimilar influence on individual semiconductor products according to oneembodiment.

FIG. 2 illustrates an exemplary hardware configuration for implementingthe flow chart depicted in FIG. 1 according to one embodiment.

FIG. 3 illustrates an exemplary 2-D (two dimensional) dependency tablein one embodiment.

FIG. 4 illustrates an exemplary 3-D (three dimensional) dependency tablein one embodiment.

FIG. 5 illustrates an example of the first table in one embodiment.

FIG. 6 illustrates an example of the second table in one embodiment.

FIG. 7 illustrates an exemplary splitting algorithm in one embodiment.

DETAILED DESCRIPTION

FIG. 1 illustrates a flow chart illustrating method steps fordetermining a group of semiconductor manufacturing process steps with asimilar influence on individual semiconductor products in oneembodiment. At step 100, a computing system (e.g., a computing system200 in FIG. 2) including at least one memory device and at leastprocessor device obtains a first table including time stamps forsemiconductor products marking their process steps in a semiconductormanufacturing process. In one embodiment, there is provided a database(not shown). The processor retrieves the first table from the database.FIG. 5 illustrates an example of the first table. In this exemplaryfirst table 500 illustrated in FIG. 5, “wafer 1” finishes a firstsemiconductor manufacturing step (“Process step 1”) at 12:10:10 PM on aparticular day. The “wafer 1” finishes a second semiconductormanufacturing step (“Process step 2”) at 12:11:10 PM on the particularday. The “wafer 1” finishes a third semiconductor manufacturing step(“Process step 3”) at 12:12:15 PM on the particular day. Although FIG. 5illustrates two wafers and three semiconductor manufacturing steps,there may be a plurality of entries for a plurality of semiconductorproducts and/or a plurality of semiconductor manufacturing steps.

At step 110, the processor creates a second table including Q-timesbased on the first table. As described above, Q-times refer to timedifferences between every successive pair of the time stamps. Thus, thesecond table includes entries describing the time differences betweenevery successive pair of the time stamps. A successive pair of stepsrefers to one step (“first step”) after the other step (“second step”).There may be other steps between the first step and the second step. Thesecond step may not be directly after the first step, vice versa. Forexample, FIG. 6 illustrates an example of the second table. Theprocessor generates this exemplary second table 600, e.g., bycalculating the time difference between successive time stamps describedin the table 500. Thus, in this exemplary second table 600, “Q-time 1”(i.e., the time difference between the process step 1 and the processstep 2) of the “wafer 1” is 1 min, i.e., 12:11:10−12:10:10=1 min.Similarly, “Q-time 2” (i.e., the time difference between the processstep 2 and the process step 3) of the “wafer 2” is 1 min 5 sec, i.e.,12:12:15−12:11:10=1 min 5 sec. Although FIG. 6 illustrates two wafersand three Q-times, there may be a plurality of entries for a pluralityof semiconductor products and/or a plurality of Q-times. Returning toFIG. 1, at step 120, the processor forms a dependency table, e.g., bygrouping the Q-times with similar dependencies together. In oneembodiment, a dependency includes, but is not limited to a correlationbetween Q-times or groups of Q-times. In one embodiment, the Q-timesaffect characteristics (e.g., leakage current, threshold voltage, etc.)of semiconductor products associated with the Q-times. In anotherembodiment, groups of Q-times affect characteristics of semiconductorproducts associated with the groups. A correlation refers to a degree ofassociation between two random variables (e.g., two different Q-times).Usually, a correlation is measured by a correlation coefficient thatranges from −1 (never occur together) through 0 (definitely independent)to 1 (always happen together). (See Jim Higgins, Ed.D., Chapter 2 in“The Radical Statistician: Unleashing The Power Of Applied Statistics InThe Real World, 2005, wholly incorporated by reference as if set forthherein, describing how to determine correlation and correlationcoefficient in detail.)

In one embodiment, the dependency table includes a multi-modalcharacter. A multi-modal character refers to a graph or histogram of adistribution of a correlation having at least two distinct maxima. In ahistogram or a density of a distribution, maxima represents the most(locally) probable values while minima represent the most (locally)improbable values. In other words, the minima are the spots where aseparation of the distribution occurs while the maxima are the spotswhere the mean of the distribution occurs (approximately). For example,an “M” shape curve is a bimodal distribution. In a further embodiment,the dependency table is a multimodal distribution. The dependency tableincludes, but is not limited to independent samples whose correlationcoefficients have unimodal distributions, and dependent samples whoseshapes change toward heavier or lighter tails. A unimodal distributionis similar to Gaussian distribution. These dependent samples may implyan extra structure (e.g., an unintended wall in a semiconductor product)and may be a possible source of information (e.g., causes of performancedegradation in a semiconductor product).

FIGS. 3-4 illustrate exemplary dependency tables in one embodiment. FIG.3 illustrates an exemplary 2-D dependency table 330. The table 330demonstrates correlations between Q-times quantized into three groups (afirst group 300, a second group 310 and a third group 320) of similarcorrelation coefficients. In one embodiment, the processor obtains theQ-times from the second table created at step 110. Each row of the table330 is a specific Q-time. Each column of the table 330 is a specificQ-time. Each element of the table is a correlation coefficient betweensuch two Q-times represented by a series of measurements (leakagecurrent, threshold voltage, etc.) for many semiconductor products. Inthe table 330, the group 300 represents low, negative correlationcoefficients (e.g., −0.5). The group 320 represents high, positivecorrelation coefficients (e.g., +0.5). The group 310 representscorrelation coefficients close to zero. Similarly, FIG. 4 illustrates a3-D exemplary dependency table 460. “X” axis 470 and “Y” axis 480 of thetable 460 are specific Q-times. “Z” axis 490 of the table 460 representsvalues of correlation coefficients. In the table 460, groups 430-450represent low, negative correlation coefficients. Groups 400-410represent high, positive correlation. Group 420 represents correlationcoefficients close to zero. The “X” axis 470, “Y” axis 480 and “Z” axis490 refer to known coordinate axes in Cartesian coordinate system.

Returning to FIG. 1, at step 130, the processor forms a third table(e.g., a 2-D, triangular table, etc.) with entries corresponding to thecorrelation coefficients and Q-times of the semiconductor manufacturingprocess. The processor identifies groups of similar dependencies. In oneembodiment, to identify the groups of similar dependencies, theprocessor clusters Q-times in the second table into groups of similardependency measures, e.g., by using a splitting algorithm and/orclustering algorithm. This clustering reduces data (e.g., Q-times) to beanalyzed to subsets of the data, e.g., by isolating the groups ofsemiconductor process steps with similar dependencies. In a furtherembodiment, a user (e.g., an engineer) may investigate the isolatedgroups to determine a physical cause (e.g., a dust in semiconductormanufacturing process, etc.) of a change in characteristics of thesemiconductor products associated with the isolated groups. In oneembodiment, the process focuses on a subspace of production logisticsdata with an application to temporary parametric device degradation(e.g., an increase of leakage current in a low nFET device, etc.). Asimilar dependency measure includes, but is not limited to a similarcorrelation coefficient. For example, a first correlation coefficientwhose value is 0.45 and a second correlation coefficient whose values is0.40 may be two similar correlation coefficients. Javed A. Aslam, etal., “The Star Clustering Algorithm for Static and Dynamic InformationOrganization,” Journal of Graph Algorithms and Applications, vol. 8, no.1, pp. 95-129, 2004, wholly incorporated by referenced as if set forthherein, describes a clustering algorithm in detail. Chen, et al.,“Domain Splitting Algorithm for Mixed Finite Element Approximations toParabolic Problems,” East-West J. Numer. Math. Vol. 1, No. 1, 1994,wholly incorporated by referenced as if set forth herein, describes asplitting algorithm in detail. In a further embodiment, there isprovided a customized splitting algorithm. This customized splittingalgorithm assumes that a distribution is a composition of several normaldistributions. This customized splitting algorithm finds the number ofcomponents (e.g., groups of similar dependencies) and their parameters(e.g., similar correlation coefficients) by best fitting to experimentaldata (e.g., samples or Q-times).

FIG. 7 illustrates an exemplary splitting algorithm in one embodiment.At step 700, a computing system (e.g., a computing system 200 in FIG. 2)receives a vector of real numbers “data” of length “D” as an input. Thecomputing system receives a number of modes “M” (for example, a defaultvalue M=2) as an input. The computing system receives an acceptabletolerance value “epsilon” (for example, a default value epsilon=1) and amaximal number of iterations “Maxcount” (for example, a default valueMaxcount=100) as inputs. The computing system receives initial values ofmeans for each mode “m=guess(:,1)”, standard deviation “sq=guess(:,2)”and distribution of modes “p=guess(:,3)” with default values: (1) m tobe “M” numbers equally spaced between minimum and maximum of data; (2)sq to be “M” numbers equal to the standard deviations of the data; and(3) p to be “M” numbers equal to 1/M. At step 710, the computing systemcalculates several iterations of the following until either“check”<“epsilon” or “count”>“Maxcount.” Each iteration includescalculating: w which is a table with M rows and D columns, where rownumber “k” is equal to the values of the density of the normaldistribution with parameters m(k) and sq(k) at points of the data. Then“w” is renormalized a couple of times (e.g., two or three times): (1)each row “k” is multiplied by “p(k)”, i.e., w(k,d):=w(k,d)*p(k); and (2)then each column is divided by its sum, i.e., w(k,d):=w(k,d)/sum_k(w(k,d)). At step 720, the computing system updates “m”, “sq” and “p” asfollows: (1) new “p” is calculated (i.e., the vector p is updated) bysumming the rows: p(m)=sum_d(w(k,d)); and (2) new “m” and “sq” arecalculated as weighted means and standard deviations of data, whereweights are the rows of w(k,d)/p(k). At step 730, a “count” is increasedby 1 (to see if the calculation did not exceed the Maxcount of number ofiterations) and “check” is calculated, e.g., as the sum of Euclideandistances of previous “m” and “updated m” and/or previous “sq” and“updated sq” and/or previous “p” and “updated p.” A smaller “check”value indicates a less number of updates on “m”, “sq” and “p”. Then, thecomputing system performs another iteration as control goes back to step710. As an output, the computing system generates a table of w(m,d)which indicates for each data(d) the probabilities of this data pointcoming from the normal distribution (mode) k, for all d=1, . . . D andk=1, . . . M together with parameters of this normal distributions andinformation of how the iterations stopped.

This exemplary algorithm further assigns each data a distribution mode(with highest probability) and hence separates the data into subsets. Inone embodiment, the data are Q-time correlations. Once the computingsystem collected the correlations into subsets, the computing system canagain analyze the meaning (e.g., Q-times, correlation coefficients,etc.) of each subset to improve semiconductor product quality (e.g.,reduced leakage current in semiconductor products).

Returning to FIG. 1, at step 140, the processor extracts semiconductormanufacturing process steps belonging to the groups of similardependencies. For example, distinctive groups (e.g., groups 400-450 inFIG. 4) are visible due to the multi-modal characteristic of thedependency table(s). In a dependency table (e.g., the table 460 in FIG.4), groups (e.g., groups 400-420 and 450 in FIG. 4) close to diagonal(e.g., a line 495 in FIG. 4) represent Q-time correlation(s) ofconsecutive (semiconductor manufacturing process) steps. Groups (e.g.,groups 430 and 440 in FIG. 4) off the diagonal represent Q-timecorrelation(s) of separate (semiconductor manufacturing process) steps.The processor may provide data (e.g., Q-times, correlation coefficients,etc.) pertaining to these groups (e.g., groups 400-450 in FIG. 4) to auser for further analysis of common physical influence on semiconductorproducts and/or of common machine or subtract features. In oneembodiment, the processor extracts the semiconductor manufacturing stepsin a particular group (e.g., a group 400 in FIG. 4), e.g., byreferencing to the first table and/or the second table.

FIG. 2 illustrates an exemplary hardware configuration of a computingsystem 200 running and/or implementing the method steps in FIG. 1. Thehardware configuration preferably has at least one processor or centralprocessing unit (CPU) 211. The CPUs 211 are interconnected via a systembus 212 to a random access memory (RAM) 214, read-only memory (ROM) 216,input/output (I/O) adapter 218 (for connecting peripheral devices suchas disk units 221 and tape drives 240 to the bus 212), user interfaceadapter 222 (for connecting a keyboard 224, mouse 226, speaker 228,microphone 232, and/or other user interface device to the bus 212), acommunication adapter 234 for connecting the system 200 to a dataprocessing network, the Internet, an Intranet, a local area network(LAN), etc., and a display adapter 236 for connecting the bus 212 to adisplay device 238 and/or printer 239 (e.g., a digital printer of thelike).

As will be appreciated by one skilled in the art, aspects of the presentinvention may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present invention may take the formof an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present invention may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with a system, apparatus, or device runningan instruction.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with asystem, apparatus, or device running an instruction.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent invention may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may run entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).

Aspects of the present invention are described below with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which run via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks. These computerprogram instructions may also be stored in a computer readable mediumthat can direct a computer, other programmable data processingapparatus, or other devices to function in a particular manner, suchthat the instructions stored in the computer readable medium produce anarticle of manufacture including instructions which implement thefunction/act specified in the flowchart and/or block diagram block orblocks.

The computer program instructions may also be loaded onto a computer,other programmable data processing apparatus, or other devices to causea series of operational steps to be performed on the computer, otherprogrammable apparatus or other devices to produce a computerimplemented process such that the instructions which run on the computeror other programmable apparatus provide processes for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more operable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be run substantiallyconcurrently, or the blocks may sometimes be run in the reverse order,depending upon the functionality involved. It will also be noted thateach block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

What is claimed is:
 1. A system for determining a group of semiconductormanufacturing process steps that have a similar influence on individualsemiconductor products, the system comprising: a memory device; and aprocessor being connected to the memory device, wherein the processorperforms steps of: obtaining a first table including time stamps of themanufacturing process steps for the individual semiconductor products;creating a second table including Q-times based on the first table, theQ-times referring to time differences between every pair of the timestamps; forming a dependency table by grouping the Q-times with similardependencies together; identifying groups of the similar dependencies;and extracting semiconductor process steps belonging to the groups. 2.The system according to claim 1, wherein the dependency table includesone of: a graph or histogram of a distribution of a correlation havingat least two distinct maxima.
 3. The system according to claim 2,wherein the identifying comprises: clustering the Q-times into thegroups of similar dependency measures.
 4. The system according to claim3, wherein the similar dependency measures include similar correlationcoefficients.
 5. The system according to claim 3, wherein the clusteringuses a splitting algorithm.
 6. The system according to claim 3, whereinthe clustering reduces data to be analyzed to subsets of the data byisolating the groups of the semiconductor process steps with the similardependencies.
 7. The system according to claim 6, wherein the processorfurther performs: investigating the isolated groups in order todetermine a physical cause of a change in characteristics of thesemiconductor products.
 8. The system according to claim 7, wherein thedependencies include correlations between the groups of the Q-times withthe characteristics of the semiconductor products.
 9. The systemaccording to claim 8, wherein groups close to a diagonal of the graph orhistogram represent correlations of consecutive semiconductormanufacturing process steps.
 10. The system according to claim 9,wherein groups off the diagonal of the graph or histogram representscorrelations of separate semiconductor manufacturing process steps. 11.The system according to claim 7, wherein the dependency table comprises:independent samples whose correlation coefficients have unimodaldistributions; and dependent samples whose shapes change toward heavieror lighter tails.
 12. The system according to claim 11, wherein theunimodal distributions is close to Gaussian distribution.
 13. A computerprogram product for determining a group of semiconductor manufacturingprocess steps with a similar influence on individual semiconductorproducts, the computer program product comprising a non-transitorystorage medium readable by a processing circuit and storing instructionsrun by the processing circuit for performing a method, the methodcomprising: generating a first table including time stamps for theindividual semiconductor products; creating a second table includingQ-times based on the first table, the Q-times referring to timedifferences between every pair of the time stamps; forming a dependencytable by grouping the Q-times with similar dependencies together;identifying groups of the similar dependencies; and extractingsemiconductor process steps belonging to the groups.